What is CAGR — Compound Annual Growth Rate Definition, Formula & Calculation

We’ll talk about the principle of compounding, go through the compound annual growth rate definition, CAGR meaning and why it’s so helpful for comparing different investments. We’ll break down the formula for compound annual growth rate and you’ll learn to calculate compound annual growth rate for any asset and for any investment period.

Hopefully by the end of the article you’ll be a ninja analyst, you will learn to define CAGR and will be able to make better decisions about the investments that are right for you.

The Compounding Principle

First things first, a word or two on compounding. There is a quote commonly attributed to Albert Einstein:

'Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it.'

We’re not sure whether the great man actually said it, but the principle really is that powerful.

You may be familiar with the concept of compound interest. Say you have $100 in a savings account with an interest rate of 10%. This rate of return is science fiction for the US, which brings us all here. But let’s say the Galaxy Far-Far Away Bank still offers an interest rate of 10% on savings. One year later, you have $110 in your account.

Now you have two options. You can either buy two transgalactic cappuccinos with cream and marshmallows from Buckstars, a large coffee chain in the Galaxy, or you can keep it in your account. If you keep it in your account, next year you get 10% on $110, the new amount, and the following year you will have 121. This will make you a millionaire in just 99 years and a billionaire after 174 short years. Not bad.

But succumb to the dark side, and you get nothing. A 100 years later you’ll still be getting 10 bucks on your $100, even if the interest rate is the same. And if you take inflation into account, your savings will be worth nothing.

This is the power of compounding. This is also why learning to invest is so important in the age of vice, misery, and low interest rates.

This also makes it important to plan to invest for the long term, rather than obsessing over Bitcoin doubling in the next 23 minutes.

So what is compound annual growth rate? Read on to find out.

What is CAGR (Compound Annual Growth Rate)?

CAGR stands for compound annual growth rate. It’s the rate at which an investment grows over a specific time period, taking the compounding factor into account, i.e. provided you don’t take out your profits at the end of each year.

CAGR definition: the rate at which an investment (or any amount) grows over a period of time, keeping in mind the compounding factor.

This is one of the most popular concepts in finance and investment. It’s a ratio that tells you how your existing or potential investment has been performing over time. However, it can apply to any figure that grows over time leading to more growth. For example, crops or altcoins with silly names.

Say an investment brings you 10% in the first year, 20% in the second year, then 30% in year 3. To work out how much this brings you on average you could add these percentages, divide them by the number of years and that would give you the average rate of return (spoiler: it doesn’t work).

In this case the average rate of return is (10%+20%+30%) / 3 = 20% on average.

But this only tells you the average percentage, without taking into consideration the original sum and what you will actually end up with at the end. Furthermore, if in one year the percentage is negative that can mess up the maths big time.

Say a $100 stock grows by 200% in one year — that’s $300. Then it loses 50% in year 2. 50% of $300 is $150.

So you can’t just add 200% and 50%, divide them by 2, and expect to know how much money you will have in two years. Because, as price changes over time, the percentage relates to growth on the new amount, not the initial one.

This is where a CAGR calculation becomes so helpful. A stock doesn’t produce a constant rate of growth every year, so CAGR gives you a single annual growth rate, a ‘smoothed’ ratio that adds up all the percentages over a period of time, say 5 years.

In fact, it doesn’t even consider the individual percentages throughout the period. It works out the average growth rate using only the beginning and the end value, but this can tell you a lot about the existing or potential growth of an investment.

Compound Annual Growth Rate Formula

Here’s the CAGR formula in all its compound glory. In case you’re not a math person, don’t be scared, we’re in this together.

To work out the compound annual growth ratio, we need to:

• Divide the ending value (EV) by the beginning value (BV)
• Raise the result to the power of 1 divided by the number of years,
• Subtract 1 from the result

Let’s break that down.

The beginning value (BV) is the sum you have at the beginning of the period;

The ending value (EV) is the sum you have at the end.

N is the number of years. So to work out the CAGR over a period of 5 years, you’ll divide the end value by the beginning value, raise the result to the power of ⅕ and subtract 1.

Raising to the power of x means to multiply a number by itself x number of times. That’s a bit like the result squared, except instead of the exponent “2” you’ll be using 1/n.

And don’t worry, you don’t have to do all of this in your brain because we’ll be using modern technology.

How to Calculate Compound Annual Growth Rate  

Let’s look at how to use the formula in real life and do a compound growth rate calculation.

We’ll work out the CAGR for 1 Google share using Google Sheets over a period of 4 years, from 2017 to 2021.

Let’s say you bought 1 Google share on 9/1/17 for $959.11. After 4 years the price went up to $2916.84.

Here’s how to calculate CAGR. Let’s put these values into Sheets using the formula: = (EV / BV) ^ (1 / n) – 1.

Then turn the result into a percentage by pressing Format > Number > Percent.

The CAGR for 1 Google share for this time period is 32.06%. This is the rate that the price of the Google stock has been growing at on average in the last 4 years.

For comparison, the total percentage growth of Google stock for the same period is 304%. But dividing this number by 4 doesn’t reflect the average return. This is why all these massive growth percentages you see online are more for marketing than for letting you know how much money you can make if you invest in a particular stock.

What can we say, Google stock looks like a pretty good investment.

Why is CAGR Important for Investors?

CAGR allows investors to quickly assess the potential of an investment to grow and fixes the limitations of the average return ratio.

Here are some ways CAGR can be used.

Goal-setting

Investors need specific goals in order to get the results they want. Say you have $10,000 to invest and you want to buy a house for $1 million in 10 years, what kinds of investments are most likely to help you achieve that goal? We can use CAGR to work that out.

Comparing potential investments

Investors can use compounded annual growth rate to quickly evaluate the performance of different stocks or different types of investments. For example, it can be used to compare stocks and bonds or stocks and ETFs.

It’s a good idea to do so against an industry median, i.e. the overall performance of an industry, such as healthcare, technology, and so on. The typical CAGR may be different in different industries.

Make sure to use the same time periods, because the overall movement of the financial markets can affect the prices of all the assets at once, which can distort your results.

Analyzing your portfolio

You can use CAGR to analyze how the different assets you hold compare in terms of their performance. CAGR analysis can simplify the complex figures you may see, especially if an asset is more volatile, i.e. its price fluctuates considerably.

Knowing what returns you can expect

CAGR can help you see past the hype around growth figures and manipulated percentages and get a realistic view of what you can expect to get over time from a particular type of investment, taking into account the compounding effect.

Limitations of CAGR

Does not predict the future

Despite being one of the best tools to estimate future growth, CAGR is not in itself a forecast of future performance. It’s important to learn as much as you can about a company

Does not take volatility into account

Since CAGR provides a smoothed rate of return on investments over a period of time, it only gives you a ratio based on the beginning and end values. It doesn’t take into account what happens in between and whether an asset is volatile or risky. The markets can have a tremendous effect on the way individual investments are performing, especially when comparing different types of assets. One market may be booming, while another may be in decline, and this may affect the CAGR even more than the performance of different companies. This is something to keep in mind when analyzing different investment options.

Not taking volatility into account can actually be a good thing for long-term investments, because it helps to get rid of all the unnecessary data and focus on what’s happening to an investment over time.

Does not reflect uneven growth

A stock price can grow 60% in one year and 10% in other years. CAGR doesn’t take that into account, that’s why it’s helpful to look at the graph to see what’s going on.

If you see that the company’s growth has slowed down, maybe it’s a sign of fundamental problems, like a decrease in demand for a commodity or a service. Then, despite the good CAGR in 5 years, this company may not be worth investing in.

You need other tools

CAGR should not be the only tool you use. Speaking of stocks, in order to identify a good investment, you’ll need to look at a company’s revenue, the price-to-earnings ratio (P/E), earnings per share (EPS) and others. It’s also good to know a bit about the company’s culture, their competition, what’s happening in the industry and the whole stock market.

Can be manipulated

Just like any financial data can be misrepresented by measuring growth from a dip to a peak, CAGR can be manipulated in the same way. If an investment has an overly impressive CAGR, e.g. 50% over 5 years, this may be due to the fact it is being measured from the time the company started or due to a recent quick rise in price despite lower previous performance.

Revenue growth CAGR and other metrics

CAGR is just a growth ratio and can be applied to any number that grows over time. One very important metric is Revenue Growth CAGR, which is a standardized form of measuring a company’s revenue, i.e. how well a company is performing.

In fact, this is much more important than the stock price. A company’s revenue reflects that a company is doing something right and the market is responding favorably. The stock price is more of a reflection of past performance combined with marketing, whereas revenue shows actual performance and is a good indication of what the stock price is likely to be in the future.

Final Thoughts

Compound Annual Revenue Growth or CAGR is a very useful formula for working out how well an investment has performed over time. Because it takes into account the compounding effect of reinvesting profits after each year, it gives good insight into how much an investor can expect to profit from a particular asset and what your overall investment returns are possible.

It’s also great for comparing assets of different classes, such as stocks, ETFs and bonds, or across different industries. In the case of comparing assets in different industries, it’s useful to know the average industry CAGR to have a point of reference.

The formula can be used for analyzing your portfolio to have the right balance of risk and return that you’re comfortable with psychologically and that will suit your goals. You can also use a CAGR calculator to make it easier.

There are many more factors and metrics to consider before making an investment decision, and we at Gainy handpicked the most important ones and arranged them in an intuitive way so that even beginners can start finding investments that are right for them.

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